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Applications of Soft Union Sets in \(h\)-Hemiregular and \(h\)-\(Intra\)-hemiregular Hemirings

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Abstract

The aim of this paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, we introduce the concepts of soft union \(h\)-\(bi\)-ideals and soft union \(h\)-\(quasi\)-ideals of hemirings by means of soft-intersection–union sum and soft-intersection–union product. Some related properties are obtained. Finally, we investigate some characterizations of \(h\)-hemiregular and \(h\)-\(intra\)-hemiregular hemirings using some kinds of soft union \(h\)-ideals.

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Acknowledgments

This research is partially supported by a grant of National Natural Science Foundation of China (11461025), Science Foundation of Hubei Province (2014CFC1125) and Key Subject of Hubei Province(Mathematics).

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Authors and Affiliations

  1. Department of Mathematics, Hubei University for Nationalities, Enshi, 445000, Hubei, China

    Jianming Zhan

  2. Institute of Mathematics, Yunnan University, Kunming, 650091, China

    Kar Ping Shum

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  1. Jianming Zhan
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  2. Kar Ping Shum
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Correspondence to Kar Ping Shum.

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Communicated by Ang Miin Huey.

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Zhan, J., Shum, K.P. Applications of Soft Union Sets in \(h\)-Hemiregular and \(h\)-\(Intra\)-hemiregular Hemirings. Bull. Malays. Math. Sci. Soc. 38, 805–825 (2015). https://doi.org/10.1007/s40840-014-0050-8

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  • DOI: https://doi.org/10.1007/s40840-014-0050-8

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